Question

Check whether 3x-7 is a factor of polynomial 6x³+x²-26x-25?

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Given: Polynomial equation $6x^{3} + x^{2} - 26x -25$

           Linear equation $3x -7$

To Check: Whether $3x - 7$ is a factor of $6x^{3} + x^{2} - 26x -25$ or not

Solution: If $3x - 7$ is a factor of $6x^{3} + x^{2} - 26x -25$, then on putting $x = \frac{7}{3}$ in the polynomial equation, the equation should become equal to 0.

Putting $x = \frac{7}{3}$ in the polynomial equation

⇒ $6(\frac{7}{3}) ^{3} + (\frac{7}{3}) ^{2} - 26(\frac{7}{3}) - 25$

⇒ $6(\frac{343}{27} ) + (\frac{49}{9}) - 26(\frac{7}{3} ) - 25$

⇒ $\frac{686}{9} + \frac{49}{9} - \frac{182}{3} - 25$

Taking L.C.M.

⇒ $\frac{686 \ + \ 49 \ - \ 546\ - \ 225}{9}$

⇒ $\frac{-36}{9}$ = $-4$

Now since, $3x - 7$ doesn't satisfy the given polynomial equation (as the equation didn't result to 0), it's not a factor of the equation.